Mathematical proof demonstrates that Lipschitz critical points of the area functional on two-dimensional domains are smooth, resolving the 1977 planar Lawson-Osserman conjecture.
We prove that if u : B₁ ⊂ R² → Rⁿ u : B 1 ⊂ R 2 → R n is a Lipschitz critical point of the area functional with respect to outer variations, then u u is smooth. This solves a conjecture of Lawson and Osserman from 1977 in the planar case.
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Hirsch et al. (2026) studied this question.
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